Isomorphism (from ancient Greek - ἴσος - "equal, identical, similar" and μορφή - "form"). Isomorphism is defined for sets endowed with some structure (for example, for groups, rings, linear spaces, etc.). In general terms it may be described as follows: an invertible mapping (bijection) between two sets endowed with a structure that is called an isomorphism if it preserves this structure.

A bijection is a mapping that is both surjective and injective. In bijective mapping, one element of a set corresponds exactly to each element of the other set, while an inverse mapping is defined that has the same property. Therefore, a bijective mapping is also called mutually identical mapping (correspondence), or one-to-one mapping.

An injection in mathematics is the mapping of set X into set Y f : : X → → Y
whereby different elements of set X are translated into different elements of set Y, that is, if two images under the mapping coincide, then the preimages also coincide:
f ( x ) = f ( y ) ⇒ ⇒ x = y

Surjection (surjective mapping, from French sur - "to", "over" + Latin jactio - "I throw") is the mapping of set X to set Y f:: X → Y
whereby each element of set Y is the image of at least one element of set X.

Isorhythm (German: Isorhythmie) is a technique of composition in European polyphonic music of the 14th and 15th centuries, expressed in the ostinato holding of a rhythmic formula, regardless of the pitch.